BUNDLED PRICES: THE EFFECT OF CURRENCY ON CONSUMER WILLINGNESS TO PAY

BUNDLED PRICES:
THE EFFECT OF CURRENCY ON
CONSUMER WILLINGNESS TO PAY



Xavier Drèze
Joseph C. Nunes*


Draft last revised January 2, 2002










Xavier Drèze is Visiting Professor of Marketing at the Anderson Graduate School of
Management, University of California, Los Angeles, CA 90095. Joseph C. Nunes is
Assistant Professor of Marketing, Marshall School of Business, University of Southern
California, Los Angeles, CA 90089-0443. The authors would like to thank Aimee Drolet
and C. W. Park for comments provided during the early stage of this paper. Both authors
contributed equally and are listed alphabetically. Questions should be directed to either
Xavier Drèze at xavier.dreze@anderson.ucla.edu or Joseph C. Nunes at
jnunes@marshall.usc.edu.

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ABSTRACT

The rising popularity of loyalty programs and related marketing promotions has
resulted in the introduction of a number of new currencies (e.g., frequent flier miles,
HHiltons Honor points) that people accumulate, budget and spend much like traditional
paper money. As consumers are increasingly able to pay for goods and services (e.g.,
airline travel, hotel stays, groceries) in more than one currency, the importance of
understanding how shoppers respond to “bundled prices,” or prices comprised of
payments delivered in multiple currencies, has become increasingly important to
marketers. This research is the first to explore how people evaluate transactions involving
prices issued in multiple currencies and when bundled prices might be superior to prices
issued in a single currency.
In this research, we explore how consumers respond to bundled prices and
determine the conditions under which a bundled price can be superior to prices charged in
a single currency. We consider a bundled price superior if it either (a) lowers the
psychological cost associated with a particular revenue objective (i.e., price), or (b) raises
the amount of revenue collected given a particular psychological cost.
First, we demonstrate how non-linear value functions open the door for optimal
bundled prices. Next we present a formal mathematical proof that outlines the conditions
under which a bundled price is superior. In Study 1, we offer experimental evidence
supporting the proposition that the subjective value of a currency other than money
(frequent flier miles) is non-linear and most likely S-shaped. In Study 2, we test the
external validity of our proofs by having real consumers (i.e., actual airline travelers)
evaluate and make choices among prices issued in single and combined currencies. The
results illustrate how bundled prices often can be superior to standard, single currency
prices.





KEY WORDS: Loyalty Programs, Pricing, Bundling, Bundled Prices, Utility Theory,
Incommensurate Resources, Mental Accounting.

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“For millions of Americans, frequent-flier miles have become a second currency. In
addition to piling them up by hopping on a plane, you can get them by making phone
calls, buying toys, investing in mutual funds, taking out a mortgage, or renting cars.”

“Meanwhile, don't be tempted by airline offers to sell you a ticket for a combination of
miles and money. The deals are usually terrible.”
Business Week
January 18, 1999



Money has been around in one form or another since at least 9000 BC, and at one
time or another cigarettes, cattle, stones, eggs, salt and porpoise teeth each has served as a
negotiable instrument (Davies 1996). Today, almost all economies run on “fiat” money,
paper notes the government says are worth something. Yet the immense popularity of
marketing promotions and loyalty programs has resulted in the introduction of several
new forms of currency that people appear to accumulate, budget and spend much like
paper money. Perhaps the most ubiquitous alternative currency in the U.S. is frequent
flier miles. More than 67 million Americans collect frequent flier miles (InsideFlyer
2001) and more than 18,500 U.S. businesses distribute miles to their customers (Business
Week 1999).
One consequence is that consumers are increasingly able to pay for things in a
combination of currencies, not just dollars. Diners Club awards two Club Rewards points
for every dollar charged, but when members don't have enough for a reward they desire,
they can charge the difference at $0.015 per point.1 Milepoint.com is an Internet
exchange site backed by a group of prominent airlines that boasts consumers can apply
frequent flier miles as partial payment towards the purchase of more than 20 million
products offered at participating merchants’ sites.2 MileShopperSM emerged as an online
catalog claiming to sell more than 300,000 brand name items from companies like
Toshiba, Samsonite and Spalding for which shoppers could apply miles for up to 30% of

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their purchases. Perhaps most familiar to frequent fliers, however, are the deals offered
by the airlines themselves. For example, American Airlines is only one of a number of
airlines that offers airline tickets for a combination of money and miles. One NetSAAver
fare advertised on their web site during the summer of 2001 offered any ticket normally
priced at $209 for the combined or “bundled price” of $49 plus 17,000 miles.

Despite the increasing popularity of prices issued in more than one currency, we
know of no work that examines how consumers evaluate “bundled prices” per se. The
concept of “bundled prices” involves combining payments in different currencies for a
single good or service, as opposed to the more common practice of “product bundling,”
in which sellers offer single units of multiple products or multiple units of the same
product for one price issued in a single currency. The two concepts are very different in
how the firm might utilize each to increase revenues. To be effective, product bundling
requires consumer heterogeneity as it is designed to take advantage of different values for
like goods across customers. In contrast, price bundling can be effective for a single
customer as a price is constructed based on the shapes of his or her idiosyncratic
valuations for the currencies involved.
In this research, we explore how consumers respond to bundled prices and
determine the conditions under which a bundled price can be superior to a price charged
in a single currency. We consider a bundled price superior if it either (a) lowers the
psychological cost associated with a particular revenue objective (i.e., price), or (b) raises
the amount of revenue collected given a particular psychological cost. In other words,
firms can benefit by either making customer feel better about what they are paying, or
charging more given the psychological cost already involved. It follows logically that a
bundled price is optimal if it minimizes the psychological cost associated with the

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maximum revenue collected, or maximizes the revenue collected associated with a given
psychological cost.

CONCEPTUAL BACKGROUND
The Value of Money and other Currencies
The idea that an optimal bundled price can exist rests on a number of well-
established economic and psychological principles. First, according to Prospect Theory
(Kahneman and Tversky 1979), an individual’s value function is believed to be concave
such that there are diminishing increases in utility for each additional equal increment in
wealth. Kahneman and Tversky take the same perspective as Bernoulli (1954), in which
(a) the particular perceptual properties are such that subjective experience is a concave
function of the magnitude of physical change, which is the same assumption made by
cardinal utility, and (b) the perceptual system is sensitive to changes in stimulus level
rather than absolute magnitudes. The assumption of diminishing marginal utility for
money is rarely contested in either psychology or economics today.3 Accordingly, a price
increase from $10 to $15 inflicts a greater psychological cost than an increase from $120
to $125 (Tversky and Kahneman 1981).
Second, research in mental accounting (Kahneman and Tversky 1984, Thaler
1980, 1985) has explored how personal financial transactions are tracked, booked (i.e.,
recorded) and posted to specific mental accounts or categories, principally in dollar
terms. Consumers are believed to set budgets for various expense accounts and as they
spend, periodically re-compute the amount of money remaining in their budgets (Heath
1995, Heath and Soll 1996). Based on how Prospect Theory’s value function compresses
large monetary magnitudes together during encoding, the marginal propensity to spend

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depends on the increment (i.e., price) and its relation to one’s perceived wealth, asset
position, or budget within a particular mental account (Thaler and Shefrin 1981, Heath
and Soll 1996). In other words, the psychological pain associated with paying an
additional $5 is expected to be greater the smaller the original amount due ($10 versus
$125), but can also be expected to seem larger the less money there is to spend, or the
smaller the amount earmarked for such expenses in an individual mental account.
Finally, research on incommensurate resources (Nunes and Park 2001) suggests
consumers react to changes in alternative currencies much like they do for money, yet
incremental costs incurred in one currency may not be judged relative to charges issued
in another currency. For example, Nunes and Park found the psychological cost
associated with surrendering 5,000 frequent flier miles on top of 50,000 miles was far
less severe than surrendering 5,000 miles on top of $500. It appears that the pain involved
in surrendering an additional 5,000 miles depends on the total miles that must be
surrendered and the number of miles in one’s frequent flier account, rather than the
amount of money one might spend or the amount of money in one’s bank account. These
results suggest consumers do not spontaneously encode frequent flier miles in dollar
terms, or vice-versa, and the units of measures or scales are not compatible (Tversky,
Sattath and Slovic 1988; Slovic, Griffin & Tversky 1990; Shafir 1995).
Consequently, just as mental accounting and mental budgeting has demonstrated
that consumers often behave as if their money were not perfectly fungible, assets
accounted for in different currencies are expected to have their own mental accounts and
be similarly non-interchangeable. Taken together, previous research suggests three
important aspects of pricing that provide the basis for bundled pricing. First, the value of
money is subject to diminishing marginal returns. Second, the marginal propensity to

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spend in one currency would depend on the amount due or the perceived asset position
within that currency. Third, the marginal propensity to spend in one currency does not
depend on the amount due or the perceived asset position in an alternative,
incommensurate currency. Therefore, opportunistic sellers can shift the balance of
payments among the currencies such that the total amount due minimizes the
psychological pain associated with the purchase.
Finally, in order for bundled prices to be effective, the firm must possess a stable
transfer function. In other words, the exchange rate must be linear for the firm (e.g., one
frequent flier mile is always equivalent to $0.02), which it uses to optimize globally over
thousands of exchanges. In 1999, Business Week (1999) advised fliers to value each of
their miles at 2 cents – most airlines’ standard selling price.4 Yet consumers who engage
in infrequent transactions (do not regularly have the opportunity to accumulate or spend
miles), or are unaware of this exchange rate, are unlikely to value their miles as such. Just
consider that consumers who paid American Airline’s fare of $49 plus 17,000 miles for a
$209 ticket received less than one cent (exactly 0.95 cents) per mile. Meanwhile, a
simultaneous offer of $79 tickets for $49 and 4,000 miles suggests someone surrendering
one-fourth the miles values each mile even less, at closer to 0.75 cents. These differences
in buy and sell rates, and among various bundled prices (see Table 1) support the
arguments that: (1) consumers don’t always utilize the value of a mile to the seller or
some stable market rate when evaluating bundled prices, and (2) a consumer’s subjective
value for miles is likely to change depending on the quantity to be surrendered.
The following example illustrates how a bundled price can be used by an airline
and be superior to one issued in a single currency. Imagine a consumer with an S-shaped
value function for miles, such that the psychological cost associated with surrendering

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1,000 miles seems negligible in dollar terms. Suppose turning over 12,500 miles feels
similar to spending $250, yet surrendering twice that amount, or 25,000 miles, is akin to
spending $600, the price of the average airline ticket. Consequently, this consumer’s
value function is convex over the range of 0 to 25,000 miles. The airline could offer a
25,000-mile ticket for the bundled price of 12,500 miles and $250, which at 2-cents per
miles brings in the equivalent revenue to the airline, yet inflicts a smaller psychological
cost to the consumer (i.e., the equivalent of $500 rather than $600).
It is critical to point out that our results depend only on non-linear valuations for
the currencies involved, and that the underlying cause or causes (e.g., wealth effects,
relativistic processing, mental accounting or budgeting, risk aversion) have no impact on
whether an optimal bundled price exists or its derivation. It is only important that (1) the
consumer does not value each unit within a currency equally; and (2) does not
spontaneously convert charges issued in one currency into increments of the other
currency, nor should they convert both simultaneously into some third currency while
evaluating a bundled price. Consequently, if the firm understands the basic shape of the
value functions for each currency (e.g., dollars and miles), using its own stable transfer
function it can determine whether a bundled price would be superior to a price issued in a
single currency. This research proves this mathematically and demonstrates it
experimentally.
The rest of this paper is organized as follows. First, we present a formal
mathematical proof that outlines the conditions under which a bundled price is superior
and alternatively when a price issued in one currency would be superior. In this section,
we outline how non-linear value functions open the door for optimal bundled prices:
those that maximize revenues while minimizing the psychological cost. Next, we present

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Study 1, which offers experimental evidence supporting our proposition that the
subjective value of a currency other than money (frequent flier miles) is non-linear, at
least for the population sampled. The results from two surveys suggest that very small
amounts of miles are not valued proportionately with large amounts, which are not valued
equivalently with much larger amounts, implying an S-shaped value function. In Study 2,
we test the external validity of the proofs by having real consumers (i.e., actual airline
travelers) evaluate and make choices among prices issued in single and combined
currencies. The results illustrate how a bundled price can be superior and how marketers
can extract higher prices from their customers, or minimize the psychological cost
associated with a particular price, through the use of bundled prices. The paper concludes
by pointing out some of the limitations of this research and offering some managerial
implications, as well as suggestions for future research.

THE USE OF BUNDLED PRICES IN MINIMIZING PERCEIVED COSTS

In this section, we show how non-linear valuations result in many instances where
marketers – in order to secure the same amount of revenue with the least amount of
psychological pain – should charge prices in a mixture of currencies (i.e., bundled
prices). We also describe situations in which a price charged in a single currency is
optimal. For simplicity and ease of exposition, we work with only two currencies: c1 and
c2. We begin by examining the case in which the value function for both currencies is
concave, followed by the case in which both are convex. We extend the discussion by
describing the case in which one is concave while the other convex, and conclude by
describing how the results differ when one currency’s value function is S-shaped.

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We assume the company possesses some transfer function (i.e., exchange rate) for
the two currencies, c1 and c2, which is linear (i.e., c = c
? ). Without a loss of generality,
1
2
we can set ? =1.5 The firm’s target price or revenue objective can be described as a
combination of c1 and c2:
R = c + c








(1)
1
2
From the consumer’s perspective, based on our assumption that consumers either do not
or cannot easily convert the two into any meaningful common unit of measurement, the
subjective value of c1 and c2 vary independently. Thus, the subjective loss or
psychological cost associated with surrendering some combination of c1 and c2 can be
written as:
E = f (c ) + g(c )







(2)
1
2
where f and g are strictly monotonically increasing continuous functions of c1 and c2,
respectively, defined over the interval [0,?] (i.e., f’ > 0 and g’ > 0). Further, f(0) = g(0) =
0, and f’, g’, f”, and g” exist over their whole domain.
Let’s assume the goal of the firm is to set a price that secures their revenue
objective while minimizing the psychological cost to the consumer. The goal could just
as easily be to maximize the revenue received given a fixed psychological cost, but
practically speaking, we expect firms to begin with established revenue objectives, not
perceived values, when developing bundled prices. Thus, the firm must solve the
optimization problem:
Min E = f (c )
( )
1 + g c2






(3)
st : c1 + c2 = r

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